7
votes
0answers
273 views

“Hard” separation results in reverse mathematics (or similar)

This is a fairly broad question. In particular, I specify 5 questions (Q1, Q2.1, Q2.2, Q3, Q4) which for me all fall under one umbrella. Since this is unreasonably broad, I'm really interested in an ...
4
votes
4answers
386 views

Strength of some claims about finitely additive measures on infinite sets?

Assume ZF. Consider the claim: (1) For any infinite set $\Omega$, there is a finitely additive probability measure $\mu:2^\Omega\to[0,1]$ with $\mu(A) = 0$ whenever $|A|<|\Omega|$. Then (1) is ...
7
votes
0answers
278 views

Fragments of Morse—Kelley set theory

Morse—Kelley set theory (hereafter MK) is the impredicative counterpart of von Neumann—Bernays—Gödel set theory (NBG), where formulas containing class quantifiers are permitted in the comprehension ...
8
votes
1answer
346 views

Weakest choice principle required for Robertson-Seymour Graph Minor Theorem?

The main Robertson-Seymour Theorem states that finite graphs form a well-quasi-ordering under the graph minor relation. In other words, in every infinite set of finite graphs, there exist two graphs ...